A sequence is defined by the following recursive equation.
Xn+1=√(2-xn) X0=0

NOTE: the n+1 is supposed to be subscript and so is the last n as well as the 0 after the x.

(a) Calculate the values of xn for n = 1, 2, 3 and 4. Report an exact answer and a decimal
approximation.
(b) Use mathematical induction to show that the even-numbered terms are increasing, that is,
that: x0 < x2 < x4 < x6 … etc.
(c) Show that the even-numbered terms are all less than

Mar 16th 2011, 10:14 AM

topsquark

Quote:

Originally Posted by turtlejacks

Here is a question that I have been stuck on.

A sequence is defined by the following recursive equation.
Xn+1=√(2-xn) X0=0

NOTE: the n+1 is supposed to be subscript and so is the last n as well as the 0 after the x.

(a) Calculate the values of xn for n = 1, 2, 3 and 4. Report an exact answer and a decimal
approximation.
(b) Use mathematical induction to show that the even-numbered terms are increasing, that is,
that: x0 < x2 < x4 < x6 … etc.
(c) Show that the even-numbered terms are all less than

How far have you gotten? And your last question got cut off.

-Dan

Mar 16th 2011, 10:51 AM

turtlejacks

oh its supposed to say less then 1. And I solved part a.
Im confused how to do part b

Mar 16th 2011, 11:42 AM

Soroban

Hello, turtlejacks!

Quote:

$\displaystyle \text{A sequence is de{f}ined by the following recursive equation:}$